Research Interests:

• Isotropic Multiresolution Analysis: smooth wavelets and frame scaling functions without directional bias in any number of dimensions, with applications to biomedical imaging (detecting vulnerable plaque in coronary arteries)
• Uncertainty principles in filter design, an almost-ideal low-pass filter with optimal time-frequency regularity properties
• Redundant encoding of vectors with frames
• Wehrl entropy and sharp uncertainty bounds for coherent state representations in mathematical physics
• Logarithmic Sobolev inequalities and phase space bounds
• Hilbert spaces with reproducing kernels
• Holomorphic representations and Berezin-Toeplitz operators
• Wiener-regularized path integrals in quantum mechanics
• Diffusion methods in sampling theory